
where the definition of the Lie bracket \(\left[\cdot ,\cdot \right]\)  can be found for example in [1]} and \(\bar{g}\left(\bar{\lambda },\bar{\eta }\right)\left(\bar{{\cal X}}\right)= \bar{g}_{\bar{{\cal X}}}\left(\bar{\lambda }_{\bar{{\cal X}}},\bar{\eta }_{\bar{{\cal X}}}\right)\) .
